This project will address methodology development needs that are important for biomarker discovery.[unreadable] evaluation, and validation. These include: (i) analysis of structure and variance in functional data (spectra[unreadable] and/or images) for biomarker discovery; (ii) evaluating the predictive values of prognostic biomarkers; and[unreadable] (iii) development of group sequential study designs and analysis methods for biomarker validation.[unreadable] First, we focus on decomposing complex functional data via wavelet and/or differential analysis. This[unreadable] analysis of coherent structure and variation allows for a refined focus on features leading to discrimination[unreadable] between disease classes.[unreadable] Second, for evaluating the predictive values of prognostic biomarkers, we propose a simple yet clinically[unreadable] relevant measure, positive predictive value (PPV) curve for survival data. Estimating and inference[unreadable] procedures of the PPV curves, the use of PPV curves for comparing predictive values of biomarkers,[unreadable] selecting models, and combining biomarkers will be studied.[unreadable] A third aim is to develop group sequential study designs and analysis "methods for biomarker validation[unreadable] studies. Focus is on developing group sequential testing and estimation methods for biomarker validation[unreadable] studies but we will also investigate group sequential testing and estimation methods for prospective[unreadable] screening studies.[unreadable] The biomarker discovery, evaluation, and validation studies in the Early Detection Research Network[unreadable] (EDRN) provide the primary motivating settings for the proposed research.